What is the difference between a UV Sphere and an Icosphere?
The major fundamental difference is how each sphere is modeled. The UV sphere, somewhat like latitude and longitude lines of the earth, uses rings and segments. Near the poles(both on the Z-axis with the default orientation) the vertical segments converge on the poles. This sphere is useful for projecting terrain onto planets and/or complex modeling as it is readily subdivided even after being created, and maps onto equirectangular projections (plate carrée) readily.
The icosphere uses a different approach. A polyhedron is made with triangles which are placed(at various subdivision levels) as an icosahedron (thus the name) and more finely-subdivided solids. All faces have the same area, which may be useful for certain types of UV mapping containing non-organic textures. An example that comes to mind is an isocahedral die or billiard balls where stretch must be minimized near the point where the number is printed onto the ball.

A conparison of UV and icospheres. UV spheres are on the left. Going downward, the subdivision levels are increased. 10 rings, 3 segments; 16/8, and 32/32 for UV spheres, and subdivision levels 1,2, and 3 for the icosphere. Default BI material is used, and light is directly behind camera.
Source: manual page and experimentation with UV mapping.